It all began in December 2012, when José Salvador Alvarenga, an El Salvadorian fisherman, boarded his 22ft fibreglass fishing boat in the village of Costa Azul on the coast of the Mexican state of Chiapas. Along with another fisherman, a teenager identified only as Ezekiel, he set off to catch sharks to sell at the market. But things started to go wrong almost immediately.

The boat's motor broke and the pair were cast adrift in the Pacific Ocean, with neither a proper water supply nor workable communication equipment. After only a month, his companion succumbed and Alvarenga is said to have pushed his corpse overboard. For 12 more months, the fisherman claims to have survived by catching fish and birds with his hands. He would pull turtles and sharks from the water, drinking their blood to stay hydrated and eating their raw flesh. Although he managed to collect water when the rains came, he is said to have survived for more than a month by drinking his own urine.

On Monday, Alvarenga was found crawling up the beach of Ebon Atoll, 6,200 miles away in the Marshall Islands. His bearded visage immediately began to fill newspapers and television bulletins. It was as if Life of Pi, Yann Martel's fantasy novel, had come true. Only in the book, Pi Patel survives at seas for 227 days – Alvarenga claims to have managed 163 more.

It is a remarkable story, made all the more so by the fact that Alvarenga looked so well as he was helped ashore to the hospital in Majuro, the capital of the Marshall Islands. He appeared ruddy, rather than burnt, and not in any way emaciated.

Perhaps inevitably, questions are now being asked about the veracity of his story. There is a log of a fishing boat going missing in Mexico in late 2012, but that particular vessel was lost in November. And the description of its occupants doesn't match Alvarenga and his companion.

Both Gee Bing, the acting Foreign Secretary of the Marshall Islands, and the American ambassador there, who acted as interpreter for Alvarenga, have been cautiously sceptical of his story. The latter, Tom Armbruster, said: "It is hard for me to imagine someone surviving 13 months at sea."

Hard, perhaps, but not impossible. There are a number of mind-bending tales of survival at sea. Steven Callahan, an American sailor on the return leg of a solo transatlantic journey in April 1982, spent 76 days adrift in the Atlantic on a 6ft life raft after his boat capsized in a collision with a whale.

A two-hour boat journey between two towns in the Kiribati islands lasted 105 days for Toakai Teitoi. He, too, was washed up near the Marshall Islands and claims to have survived on raw fish and rain water. He put his final rescue by a passing boat down to the ministrations of a shark, however. "If a shark hadn't nudged me awake, the crew of the boat might have thought I wasn't in trouble and might have carried on sailing past me," he said at the time of his rescue in 2012.

The longest time spent alone adrift, however, was 133 days. After 25-year-old Poon Lim's merchant ship was sunk by a German U-boat off the coast of Cape Town in 1942, he drifted across the entire Atlantic on a life raft, fetching up at the mouth of the Amazon.

It is worth noting that if Alvarenga's tale is to believed, he would have been at sea 259 days more than Lim. Is that credible? Views are mixed. According to Dr Simon Boxall, an oceanographer from the University of Southampton, it is definitely feasible.

"If you check the charts, you see that the flow of the current would take you from Mexico to the Marshall Islands. And the time frame fits, too: he would need only to be going at half a mile per hour, which is reasonable if he had the wind behind him."

Jeya Henry, a professor of nutrition at Oxford Brookes University, says a diet of raw fish and birds might also be enough to prevent death by starvation. "The human body is extremely resilient to food deprivation. The body is well adapted to survive long periods on restricted food intake," he says.

Survival experts, though, have been left scratching their heads. James Mandeville, a former army officer and expert in survival at sea, explains that he would expect to see certain ailments on the fisherman. "If he was using his hands to catch fish, they would be covered in sores from the salt water and bacteria in the sea. His eyesight would also have deteriorated from the glint of the sun on the water," he says.

Mandeville is most sceptical, though, about Alvarenga's claim to have saved enough water to survive for a month when there was no rain. "You couldn't survive for long drinking urine and turtle blood – it would finish off the kidneys and liver – and with the temperatures in the Pacific, you would need two to three litres of water per day to survive. He would need a very big water container," he says.

If Alvarenga's story can be proved, and proof in such cases is elusive, this may yet turn out to be the most extraordinary tale of survival ever known. Otherwise, it might just as well prove to be one of the best-publicised fish stories of modern times.